The moderators asked a question about Trump’s 2017 executive order barring immigrants from seven predominantly Muslim countries. That order led to nationwide protests and was highly divisive: 53% of Americans in a CNN/ORC poll said they opposed it at the time, while 47% said they supported it.

-Analysis by Nathaniel Rakich of 538

Crossing into the second hour of the debate, attention turned to Trump as Haley was asked if she agreed with his plan to bring back and expand his restrictions on immigration from Muslim countries.

Haley said there shouldn't be a straight ban on immigrants from Muslim countries, but rather a review of countries that have terrorist activity and represent a threat to the U.S.

"You look at what came across the southern border, what worries me the most are those that came from Iran, from Yemen, from Lebanon, those areas where they say 'death to America,'" she said. "That's where you want to be careful. It's not about a religion. It's about a fact that certain countries are dangerous and are threats to us."

DeSantis then stepped in, saying he would take it further.

"It's not just terrorism though," DeSantis said, adding: "There needs to be limits on immigration, and we should not be importing people from cultures that are hostile."

-ABC News' Alexandra Hutzler

The candidates were asked how tough they will be on high immigration at the southern border -- including the issues of unauthorized crossings and fentanyl being smuggled in.

DeSantis defended comments that he would order the military to shoot suspected drug smugglers "stone cold dead," despite critics saying that would violate the law, and he said he supports building a wall across the southern border

"The commander in chief not only has a right, you have a responsibility to fight back against these people," he said.

Haley was asked to clarify her stance on whether she would deport all unauthorized migrants. She said the U.S. has to "stop the incentive of what's bringing them over here in the first place" -- noting that President Joe Biden recently gave temporary protective status to 500,000 Venezuelans -- and also vet those who are in the country, for instance, based on their tax and employment status.

On the fentanyl overdose crisis, she turned to China, saying, "We need to end all normal trade relations with China until they stop murdering Americans with fentanyl."

Ramaswamy was asked how effective his policy to use the military to "annihilate drug labs inside Mexico" would be.

"I don't think it’s going to have to come to that if we deal with the actual demand-side problem that we also have in this country," he said. "I mean, the easy part is talking about how we’re going to use our military to secure the border. I will, and I believe that everybody else wants to do the same thing. But the harder part is dealing with the crisis of purpose and meaning, the mental health epidemic raging across the country like wildfire."

He also pointed to China as a source of fentanyl, saying, "We also have to hold them accountable with every financial lever that we have available."

-ABC News' Meredith Deliso

Haley lamented the state of economy, promising to veto any spending bill that doesn’t take federal expenditures to pre-COVID-19 levels. She slammed the Trump administration for adding $9 trillion to the federal debt.

DeSantis wouldn’t directly target Trump but chalked the the problem up to “both parties in Washington, D.C. That’s just a fact.” He pointed to student loans as an economic backbreaker for young people and touted his record on vocational education, which he said could encourage universities to become more accessible: “Don’t let anybody tell you the only way you can be successful is through a four-year, brick-and-ivy degree. That’s one way you could be, not the only way, and we’re gonna fix that problem in the United States of America.”

- ABC News’ Chris Boccia

At the beginning of the year, DeSantis was the clear runner-up in the Republican presidential primary field: He was averaging above 30% in national polls, only about 10 points behind Trump. But DeSantis’ star has fallen the more voters have gotten to know him, it seems, and another candidate is now on the verge of overtaking him as the most viable Trump alternative: Haley.

As of Tuesday, Haley was at 11% in 538’s national polling average of the Republican primary -- just 2 points behind DeSantis for second place. And she’s doing even better in early primary states. She’s polling at 15% in Iowa, and she’s comfortably in second place in New Hampshire (19%) and South Carolina (21%).

She also recently secured the endorsement of Americans for Prosperity Action, a conservative group affiliated with Republican megadonor Charles Koch that is known for its sophisticated political operation.

Why has Haley been on the upswing? The simplest explanation is these debates. On the day of the first debate, she was averaging just 3% in national polls. But according to a 538/Washington Post/Ipsos poll conducted both before and after that debate, Republicans who watched said Haley was one of the strongest performers, and the share who said they were considering voting for her shot up by 17 points.

Republican debate watchers also rated Haley as the second-best performer in the second debate and the strongest performer in the third debate. Probably not by coincidence, her polling numbers have been steadily increasing ever since.

Of course, Haley fans shouldn’t get too giddy. She (and DeSantis) are still far behind Trump both nationally and in the early primary states. Even if Haley does overtake DeSantis and winds up being the last non-Trump Republican standing in the primary, it won’t matter if Trump is winning every state by double digits.

-Analysis by Nathaniel Rakich of 538